Lumped element circulator having a plurality of separated operation bands

ABSTRACT

A lumped element circulator having a plurality of operation bands, has a circulator element with a plurality of signal ports and a grounded terminal, and resonance circuits connected between the signal ports and the grounded terminal, respectively, each of the resonance circuits having a plurality of resonance points. The number of the operation bands is equal to the number of the resonance points of each of the resonance circuits.

FIELD OF THE INVENTION

The present invention relates to a lumped element circulator used as a high frequency circuit element in for example a portable or mobile communication equipment. Particularly, the present invention relates to a lumped element circulator operable in a plurality of frequency bands.

DESCRIPTION OF THE RELATED ART

A circulator is an element for giving non-reciprocal characteristics to a high frequency circuit so as to suppress reflecting waves in the circuit. Thus, standing waves can be prevented from generation resulting that stable operations of the high frequency circuit can be expected. Therefore, in recent portable telephones, such non-reciprocal elements are usually provided for suppress standing waves from generation.

Recently, demand for a portable telephone capable of operating in a plurality of different frequency bands (multi-bands telephone) has been increased in order to enable effective use of the portable telephone. However, the conventional circulator can be operated in only one frequency band. Thus, in order to operate in a plurality of frequency bands, it is necessary (A) to broaden the frequency bandwidth of the single band circulator by using an impedance matching circuit, or (B) to combine a plurality of single band circulators with a band-pass filter for individually operating the circulators.

According to the above-mentioned solution (A) where the frequency bandwidth of the single band circulator is broadened, a sufficiently wide bandwidth cannot be expected but only about 30% of the center frequency can be broadened. Thus, as for a recent dual band portable telephone operable at dual frequencies which differ twice with each other, the solution (A) cannot be adopted.

According to the solution (B) where a plurality of single band circulators operating at different frequency bands are connected in parallel and are selected by filters and switching means, the dimension of the combined circuit becomes large. In addition, the impedance characteristics out of the bandwidths of the circulators interfere with each other causing the operating characteristics to become unstable.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a lumped element circulator which alone can suppress standing waves from generation in a plurality of frequency bands.

According to the present invention, a lumped element circulator having a plurality of operation bands, has a circulator element with a plurality of signal ports and a grounded terminal, and resonance circuits connected between the signal ports and the grounded terminal, respectively, each of the resonance circuits having a plurality of resonance points. The number of the operation bands is equal to the number of the resonance points of each of the resonance circuits.

The invention focuses attention on that, in a lumped element circulator, difference between eigenvalues of the circulator element excited by positive and negative rotational eigenvectors is 120 degrees (in case of three port circulator) without reference to frequency. Thus, according to the invention, a network exhibiting a frequency performance for satisfying circulator conditions in a plurality of necessary frequency bands is connected to each port so that the circulator can operate in the plurality of frequency bands. This is realized by inserting a resonance circuit having a plurality of resonance points between each of the signal ports and the grounded terminal of the circulator element of the lumped element circulator.

As a result, according to the invention, a lumped element circulator alone can suppress any standing wave from generation in a plurality of frequency bands. Thus, in a high frequency circuit in a telephone which operates in a plurality of frequency bands such as a dual band telephone, the circulator according to the present invention can be alone used to suppress standing wave from generation in a plurality of frequency bands.

It is preferred that each of the resonance circuits is a series-parallel resonance circuit having at least one pair of a series resonance point and a parallel resonance point.

It is also preferred that the number of the operation bands is equal to the number of the pair of the series resonance point and the parallel resonance point plus one.

Further objects and advantages of the present invention will be apparent from the following description of the preferred embodiments of the invention as illustrated in the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an oblique view schematically illustrating a structure of a dual band lumped element circulator of a preferred embodiment according to the present invention;

FIG. 2 shows an equivalent circuit diagram of the lumped element circulator of the embodiment shown in FIG. 1;

FIG. 3 shows an equivalent circuit diagram of a conventional lumped element circulator;

FIGS. 4a and 4 b show a sectional view and a top view illustrating a structure of an inductor part of the conventional lumped element circulator:

FIG. 5 shows an exploded oblique view illustrating a structure of a circulator element part of the conventional lumped element circulator;

FIG. 6 shows an oblique view illustrating an assembled structure in which resonance capacitors are connected to the circulator element shown in FIG. 5;

FIG. 7 illustrates magnetic field intensity when current flows through each signal port;

FIG. 8 shows a Smith chart illustrating variations of eigenvalues by connecting the resonance capacitors to satisfy the circulator conditions;

FIG. 9 shows a Smith chart illustrating that y₃−y₂ is independent of frequency;

FIG. 10 shows a circuit diagram illustrating a resonance circuit connected to each port of the lumped element circulator of the embodiment shown in FIG. 1;

FIG. 11 illustrates frequency-admittance characteristics of the resonance circuit shown in FIG. 10;

FIG. 12 illustrates transfer characteristics of a dual band lumped element circulator actually designed and fabricated; and

FIG. 13 shows a circuit diagram illustrating each of resonance circuits connected to a lumped element circulator of another embodiment according to the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 schematically illustrates a structure of a three port type dual band lumped element circulator of a preferred embodiment according to the present invention.

In the figure, reference numerals 10 and 11 denote integrated ferromagnetic material disks, made of for example ferrite, sandwiching three pairs of two parallel drive conductors 12 ₁, 12 ₂ and 12 ₃ which are insulated from each other, 13 and 14 denote shielding electrodes formed on outer surfaces of the respective ferromagnetic material disks 10 and 11, 15 denotes a grounded electrode, 16 ₁, 17 ₁, 16 ₃ and 17 ₃ denote resonance capacitors, and 18 ₁ and 18 ₃ denote resonance coils, respectively. The pairs of drive conductors 12 ₁, 12 ₂ and 12 ₃ constitute three inductors which extend to three directions 120 degrees apart and form a trigonally symmetric shape.

The resonance capacitor 17 ₁ and the resonance coil 18 ₁ constitute a series resonance circuit. This series resonance circuit and the resonance capacitor 16 ₁ are connected in parallel between the signal port of the drive conductor pair 12 ₁ and the grounded electrode 15. Similar to this, the resonance capacitor 17 ₃ and the resonance coil 18 ₃ constitute a series resonance circuit. This series resonance circuit and the resonance capacitor 16 ₃ are connected in parallel between the signal port of the drive conductor pair 12 ₃ and the grounded electrode 15. Although it is hidden in FIG. 1, a series resonance circuit which is constituted by the resonance capacitor 17 ₂ and the resonance coil 18 ₂, and the resonance capacitor 16 ₂ (FIG. 2) are connected in parallel between the signal port of the drive conductor pair 12 ₂ and the grounded electrode 15. Excitation permanent magnets (not shown) are provided on the element 10 and under the element 11, respectively.

An equivalent circuit of the lumped element circulator of the embodiment of FIG. 1 is illustrated in FIG. 2. As will be understood from this figure, this lumped (element circulator is equivalent to a circuit in which, between signal ports 21 ₁, 21 ₂ and 21 ₃ of an ideal circulator 20 and the grounded electrode 15, a series-parallel resonance circuit constituted by the resonance capacitor 16 ₁ with a capacitance C₀, the resonance capacitor 17 ₁ with a capacitance C₁, the resonance coil 18 ₁ with an inductance L₁ and an inductor L, a series-parallel resonance circuit constituted by the resonance capacitor 16 ₂ with a capacitance C₀, the resonance capacitor 17 ₂ with a capacitance C₁, the resonance coil 18 ₂ with an inductance L₁ and an inductor L, and a series-parallel resonance circuit constituted by the resonance capacitor 16 ₃ with a capacitance C₀, the resonance capacitor 17 ₃ with a capacitance C₁, the resonance coil 18 ₃ with an inductance L₁ and an inductor L are connected, respectively. The ideal circulator 20 is a virtual circuit element operating as a circulator over whole range from zero frequency to infinite frequency. The circuit composed of this ideal circulator 20 and the inductors L corresponds to non-reciprocal inductance of the meshed drive conductors 12 ₁, 12 ₂ and 12 ₃ constructed in the circulator element.

According to the lumped element circulator of this embodiment, instead of a capacitor, the resonance circuit providing a necessary effective capacitance at required frequencies is connected between each of the signal ports 21 ₁, 21 ₂ and 21 ₃ and the grounded electrode 15. Thus, this lumped element circulator can operate as a circulator in a plurality of frequency bands, as described hereinafter in detail.

An equivalent circuit of a conventional lumped element circulator is illustrated in FIG. 3. As shown in this figure, the conventional lumped element circulator is equivalent to a circuit in which parallel resonance circuits 32 ₁, 32 ₂ and 32 ₃ with a center frequency f₀ are connected to signal ports 31 ₁, 31 ₂ and 31 ₃ of an ideal circulator 30, respectively. The ideal circulator 30 is a virtual circuit element operating as a circulator over whole range from zero frequency to infinite frequency. The circuit composed of this ideal circulator 30 and inductors L in the parallel resonance circuits 32 ₁, 32 ₂ and 32 ₃ corresponds to non-reciprocal inductance of meshed drive conductors constructed in a circulator element of the conventional lumped element circulator.

FIGS. 4a and 4 b illustrate a structure of an inductor part of the conventional lumped element circulator, FIG. 5 illustrates a structure of a circulator Element part of this conventional lumped element circulator, and FIG. 6 illustrates an assembled structure in which resonance capacitors are connected to the circulator element shown in FIG. 5.

As will be apparent from these figures, the structure of the circulator element part of this conventional lumped element circulator is the same as that of the lumped element circulator of the embodiment shown in FIG. 1.

Namely, integrated ferromagnetic material disks 40 and 41 sandwich three pairs of two parallel drive conductors 42 ₁, 42 ₂ and 42 ₃ which are insulated from each other. Shielding electrodes 43 and 44 are formed on outer surfaces of the respective ferromagnetic material disks 40 and 41. The drive conductor pairs 42 ₁, 42 ₂ and 42 ₃ constitute three inductors which extend to three directions 120 degrees apart and form a trigonally symmetric shape. Resonance capacitors 46 ₁, 46 ₂ and 46 ₃ are connected between signal ports 31 ₁, 31 ₂ and 31 ₃ of the drive conductor pairs 42 ₁, 42 ₂ and 42 ₃, respectively. Excitation permanent magnets 47 and 48 are provided on the element 40 and under the element 41, respectively.

In FIG. 4a, a section of the inductor (drive conductor 42 ₁) connected to one signal port (signal port 31 ₁ for example) and excited magnetic fields are illustrated. Suppose that inductance of this inductor (drive conductor pair 42 ₁) is L₀, magnetic field 49 excited by current flowing through the remaining two inductors (drive conductor pairs 42 ₂ and 42 ₃) will cross the inductor 42 ₁ connected to the signal port 31 ₁. Thus, inductance viewed from this signal port 31 ₁ has to be calculated in consideration of the influence of the magnetic field 49.

In a n-ports circuit, reflection coefficients of respective signal ports can be equalized with each other by applying specially combined advance waves to the respective signal ports. Vectors indicating the advance waves which satisfy this condition are called as eigenvectors, and the reflection coefficients are called as eigenvalues. In the n-ports circuit, n eigenvectors and n eigenvalues corresponding to the respective vectors are existed. Therefore, in the three ports circulator, three eigenvectors u₁, u₂ and u₃ and three eigenvalues s₁, s₂ and s₃ corresponding to the respective vectors are existed. These eigenvectors should have the following values. $\begin{matrix} \begin{matrix} {{{\overset{\rightarrow}{u}}_{1} = \quad {\frac{1}{3}\begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}}},{{\overset{\rightarrow}{u}}_{2} = {\frac{1}{3}\begin{pmatrix} 1 \\ ^{{- j}\quad \frac{2\pi}{3}} \\ ^{\quad {j\quad \frac{2\pi}{3}}} \end{pmatrix}}},{{\overset{\rightarrow}{u}}_{3} = {\frac{1}{3}\begin{pmatrix} 1 \\ ^{j\quad \frac{2\pi}{3}} \\ ^{{- j}\quad \frac{2\pi}{3}} \end{pmatrix}}}} \\ {{s_{2} = \quad {s_{1}^{\quad {j\quad \frac{2\pi}{3}}}}},{s_{3} = {s_{1}^{{- j}\quad \frac{2\pi}{3}}}}} \end{matrix} & (1) \end{matrix}$

Admittances y₁, y₂ and y₃ with respect to these reflection coefficients are given as following equation (2); $\begin{matrix} {{y_{i} = {Y_{c}\quad \frac{1 - s_{i}}{1 + s_{i}}}},\quad \left\lbrack {{i = 1},2,3} \right\rbrack} & (2) \end{matrix}$

where Y_(c) is the terminal admittance of each port.

In case that the magnetic field H₁ excited by current j₁ flowed into the signal port 31 ₁ of the conventional lumped element circulator shown in FIGS. 3 to 6 is as indicated by the dotted line arrow 49 in FIG. 4b, the magnetic fields H₂ and H₃ excited by currents j₂ and j₃ flowed into the ports 31 ₂ and 31 ₃ respectively are represented, by using H₁ as a reference, as shown in FIG. 7. Thus, it is apparent that H₁ direction components of the magnetic fields H₂ and H₃ are represented as; $\begin{matrix} \begin{matrix} {{{- {\overset{.}{H}}_{2}}\cos \quad \frac{\pi}{3}} = {{- \frac{1}{2}}\quad {\overset{.}{H}}_{2}}} \\ {{{- {\overset{.}{H}}_{3}}\cos \quad \frac{\pi}{3}} = {{- \frac{1}{2}}\quad {\overset{.}{H}}_{3}}} \end{matrix} & (3) \end{matrix}$

and then, by adding the magnetic field H₁, the magnetic field H is represented by following equation (4). $\begin{matrix} {H = {{\overset{.}{H}}_{1} - {\frac{1}{2}\left( {{\overset{.}{H}}_{2} + {\overset{.}{H}}_{3}} \right)}}} & (4) \end{matrix}$

Thus, excitation magnetic fields H¹, H² and H³ for the respective eigenvectors u₁, u₂ and u₃ are obtained by following equations (5); $\begin{matrix} \begin{matrix} {H^{1} = {{{\overset{.}{H}}_{1} - {\frac{1}{2}\left( {{\overset{.}{H}}_{1} + {\overset{.}{H}}_{1}} \right)}} = 0}} \\ {H^{2} = {{{\overset{.}{H}}_{1} - {\frac{1}{2}\left( {{^{{- j}\quad \frac{2\pi}{3}}{\overset{.}{H}}_{1}} + {^{\quad {j\quad \frac{2\pi}{3}}}{\overset{.}{H}}_{1}}} \right)}} = {\frac{3}{2}\quad {\overset{.}{H}}_{1}}}} \\ {H^{3} = {{{\overset{.}{H}}_{1} - {\frac{1}{2}\left( {{^{{- j}\quad \frac{2\pi}{3}}{\overset{.}{H}}_{1}} + {^{\quad {j\quad \frac{2\pi}{3}}}{\overset{.}{H}}_{1}}} \right)}} = {\frac{3}{2}\quad {\overset{.}{H}}_{1}}}} \end{matrix} & (5) \end{matrix}$

therefore, inductances of the conductors viewed from the respective signal ports L₁, L₂ and L₃ for the eigenvectors u₁, u₂ and u₃ are given as following equation (6); $\begin{matrix} {{L_{1} = 0},{L_{2} = {L_{3} = {{\frac{3}{2}\quad L_{0}} \equiv \xi}}}} & (6) \end{matrix}$

where L₀ is the inductance of the shorten end two parallel conductors connected to one signal port when another conductors are open at end behalf of shorten.

The loading admittances of the ferromagnetic material disk or the ferrite, in other words the admittances of the part of the inductor y_(L1), y_(L2) and y_(L3) for the eigenvectors u₁, u₂ and u₃ are therefore given as following equation (7); $\begin{matrix} \begin{matrix} {y_{L1} = \infty} \\ {y_{L2} = \frac{1}{j\quad \omega \quad \xi \quad \mu_{+}}} \\ {y_{L3} = \frac{1}{j\quad \omega \quad \xi \quad \mu_{-}}} \end{matrix} & (7) \end{matrix}$

where μ₊ and μ⁻ are the positive and the negative polarized relative permeabilities. It is to be noted that the magnetic filed for exciting the eigenvectors u₂ and u₃ become the positive and negative rotational magnetic fields with respect to the externally applied D.C. magnetic field. The values μ₊ and μ⁻ are obtained by Polder's equation as following equation (8); $\begin{matrix} \begin{matrix} {\mu_{\pm} = {1 + \frac{P}{\sigma \mp 1}}} \\ {{P = \frac{{\gamma }4\pi \quad M_{s}}{\omega}},} \\ {\sigma = \frac{{\gamma }\quad H_{i}}{\omega}} \end{matrix} & (8) \end{matrix}$

where 4πM_(s) is the saturation magnetization of the ferrite, H_(i) is the internal D.C. magnetic field in the ferrite, and γ is the gyromagnetic constance. By using the equation (8), following equation (9) can be obtained. $\begin{matrix} {{\frac{1}{\mu_{-}} - \frac{1}{\mu_{+}}} = {{\frac{\sigma + 1}{\sigma + 1 + P} - \frac{\sigma + 1}{\sigma - 1 + P}} = \frac{2P}{\left( {\sigma + P} \right)^{2} - 1}}} & (9) \end{matrix}$

When it is operated under a magnetic field which is higher than the ferromagnetic resonance field (under above-resonance operation), for example operated in the lumped element circulator, there is a relationship of (σ+P)²>>1. Therefore, in this case, the equation (9) can be made approximations as follows. $\begin{matrix} {{\frac{1}{\mu_{-}} - \frac{1}{\mu_{+}}}\overset{.}{\underset{.}{=}}{\frac{2\omega {\gamma }4\pi \quad M_{s}}{{\gamma }^{2}\left( {H_{i} + {4\pi \quad M_{s}}} \right)^{2}} = \frac{8{\omega\pi}\quad M_{s}}{{\gamma }\left( {H_{i} + {4\pi \quad M_{s}}} \right)^{2}}}} & (10) \end{matrix}$

As a result, a value of (1/jωξμ₊)−(1/jωξμ⁻) can be obtained by following equation (11); $\begin{matrix} {{\frac{1}{j\quad \omega \quad {\xi\mu}_{-}} - \frac{1}{j\quad \omega \quad {\xi\mu}_{+}}} = {{y_{L3} - y_{L2}} = \frac{8\pi \quad M_{s}}{j\quad \xi {\gamma }\left( {H_{i} + {4\pi \quad M_{s}}} \right)^{2}}}} & (11) \end{matrix}$

where the value of j(y_(L2)-y_(L3)) is not related to frequency. This result suggests that the difference between the eigenvalues s₂ and s₃ in the circulator under excitation of the eigenvectors u₂ and u₃ is independent to frequency. In the lumped element circulator, the inductance L₁ for the eigenvector u₁ is 0 as indicated in the equation (6). Thus, the eigenvalue s₁ is located at the right end point (1,0) on the Smith chart and independent to frequency. Therefore, after the applied magnetic field is adjusted so that the eigenvalues s₂ and s₃ have 120 degrees apart from each other on the Smith chart, if the position of the eigenvalues s₂ and s₃ are moved by adding capacitors to the respect signal ports so that the angle of each of the eigenvalues s₂ and s₃ with respect to the eigenvalue s₁ becomes 120 degrees as shown in FIG. 8, a complete circulator at that frequency can be obtained.

In order to realize a circulator, it is necessary for the lumped element circulator that the eigenvalues s₂ and s₃ have to satisfy following equation (12) derived from the conditions of the eigenvalue s₁ expressed by the equation (7) with reference to the equation (1). $\begin{matrix} {{s_{1} = {- 1}},{s_{2} = ^{{- j}\quad \frac{\pi}{3}}},{s_{3} = ^{j\quad \frac{\pi}{3}}}} & (12) \end{matrix}$

Eigenadmittances satisfying this condition are given as following equation (13). $\begin{matrix} {{y_{1} = \infty},{y_{2} = {{- j}\quad \frac{Y_{c}}{\sqrt{3}}}},{y_{3} = {j\quad \frac{Y_{c}}{\sqrt{3}}}}} & (13) \end{matrix}$

Thus, $\begin{matrix} {{y_{3} - y_{2}} = {j\quad \frac{2Y_{c}}{\sqrt{3}}}} & (14) \end{matrix}$

is given. Substituting this equation (14) into the equation (11), following equation (15) is obtained. $\begin{matrix} {\xi = \frac{4\sqrt{3}\pi \quad M_{s}Z_{c}}{{\gamma }\left( {H_{i} + {4\pi \quad M_{s}}} \right)^{2}}} & (15) \end{matrix}$

It should be noted from the equation (13) that the circulator has to satisfy y₂+y₃=0. This is equivalent to that, as shown in FIG. 9, the admittances on the Smith chart are replaced as y_(L2)→y₂ and y_(L3)→y₃ with keeping the relation of the equation (14) to satisfy the circulator conditions by adding resonance capacitors to the signal ports, respectively. Therefore, the condition of (y₂+y₃)/2=ωC should be held. This condition can be obtained as follows by using the equation (8) and the above-resonance operation conditions of σ², σP>>1. $\begin{matrix} \begin{matrix} {\frac{y_{L3} + y_{L2}}{2} = \quad {\frac{1}{j\quad 2\omega \quad \xi}\left( {\frac{1}{\mu_{-}} + \frac{1}{\mu_{+}}} \right)}} \\ {= \quad \frac{\sigma^{2} - 1}{j\quad \omega \quad \xi \quad \left( {\sigma^{2} - 1 + {\sigma \quad P}} \right)}} \\ {\overset{.}{\underset{.}{=}}\quad \frac{\sigma}{j\quad \omega \quad \xi \quad \left( {\sigma + \quad P} \right)}} \\ {= \quad {\omega \quad C}} \end{matrix} & (16) \end{matrix}$

As a result, the capacitance C can be obtained by following equation (17). $\begin{matrix} {C = {\frac{\sigma}{\omega^{2}{\xi \left( {\sigma + P} \right)}} = \frac{H_{i}}{\omega^{2}\xi \quad \left( {H_{i} + {4\pi \quad M_{s}}} \right)}}} & (17) \end{matrix}$

If a resonance capacitor with the capacitance C which is inversely proportional to ω² is connected to each port, it is possible to obtain a circulator. In other words, if a circuit exhibiting a required effective capacitance at required frequencies is connected each port of the circulator element, a desired circulator having a plurality of operating frequency bands can be realized.

Suppose that a circulator is realized by connecting a circuit exhibiting the capacitance C at the frequency f₁ to each port. A circulator operating at both frequencies f₁ and f₂ can be obtained by connecting to each port of this circulator a circuit exhibiting a capacitance C at the frequency f₁ and also exhibiting a capacitance (f₁/f₂)²C at the frequency f₂.

A series-parallel resonance circuit shown in FIG. 10 is capacitive under and above the resonance frequency. Thus, if the operating frequencies of this circuit are adjusted at frequencies under and above its series-parallel resonance frequency, this circuit will meet the above-mentioned condition. An admittance y of this series-parallel resonance circuit is given as; $\begin{matrix} {y = {{j\quad \omega \quad C_{0}} + \frac{1}{{j\quad \omega \quad L_{1}} - \frac{1}{j\quad \omega \quad C_{1}}}}} & (18) \end{matrix}$

which is expressed as the frequency-admittance characteristics shown in FIG. 11. This equation (18) can be rewritten as; $\begin{matrix} {y = \frac{\omega \quad {C_{0}\left( {\omega_{p}^{2} - \omega^{2}} \right)}}{\omega_{s}^{2} - \omega^{2}}} & (19) \end{matrix}$

where ω_(s) and ω_(p) are angular frequencies of the series resonance and the parallel resonance, respectively, and ${\omega_{s}^{2} = \frac{1}{L_{1}C_{1}}},\quad {\omega_{p}^{2} = {\omega_{s}^{2}\quad \left( {1 + \frac{C_{1}}{C_{0}}} \right)}}$

In the case of f₂=2f₁, a necessary capacitance is C/4 and therefore the admittances at the frequencies f₁ and f₂ are expressed as ω₁C and ω₂C=ω₁C/2, respectively. Substituting these conditions into the equation (19), following equations are obtained. $\begin{matrix} {{{\omega_{1}C} = \frac{\omega \quad {C_{0}\left( {\omega_{p}^{2} - \omega^{2}} \right)}}{\omega_{s}^{2} - \omega^{2}}}{\frac{\omega_{1}C}{2} = \frac{\omega \quad {C_{0}\left( {\omega_{p}^{2} - \omega^{2}} \right)}}{\omega_{s}^{2} - \omega^{2}}}} & (20) \end{matrix}$

Since the number of unknowns is more than the number of equations in the equation (20), some constants in the equation can be arbitrarily determined. If x and y are expressed as; ${x = \frac{\omega_{s}}{\omega_{1}}},\quad {y = \frac{\omega_{p}}{\omega_{1}}}$

in case of f₂=2f₁, y is given by following equation (21). $\begin{matrix} {y = \sqrt{5 - \frac{4}{x^{2}}}} & (21) \end{matrix}$

The x and y are restricted as 1<x<2 and 1<y<2 because of the predetermined relation between the operation frequencies and, as will be apparent from FIG. 11, the solution will be unstable when x approaches 1 or y approaches 2. By determining y after x is determined to an appropriate value, C₀, C₁ and L₁ can be obtained from the equation (20) as follows. $\begin{matrix} \begin{matrix} {C_{0} = {C\quad \frac{x^{2} - 1}{y^{2} - 1}}} \\ {C_{1} = {{C_{0}\left\{ {\frac{y^{2}}{x^{2}} - 1} \right\}} = {C\quad \frac{x^{2} - 1}{y^{2} - 1}\quad \left\{ {\frac{y^{2}}{x^{2}} - 1} \right\}}}} \\ {L_{1} = {\frac{1}{\omega_{s}^{2} \cdot C_{1}} = \frac{1}{\left( {x \cdot \omega_{1}} \right)^{2} \cdot C_{1}}}} \end{matrix} & (22) \end{matrix}$

A dual band lumped element circulator according to this embodiment is practically designed and fabricated. To design the circulator, when we choose values of 4πM₃=400 Gauss, f₁=300 MHz, σ=3.5 and Zc=50Ω, P, ωξ and ξ are calculated as follows. $\begin{matrix} {P = {\frac{2.8 \times 450}{300} = 4.20}} \\ {{{\omega \quad \xi} = {\frac{\sqrt{3} \times 4.20 \times 50}{\left( {3.50 + 4.20} \right)^{2}} = {6.13\quad (\Omega)}}}\quad} \end{matrix}$

 ξ=3.25(nH)

Thus, the resonance capacitance C can be obtained by using the equation (17) as follows. $\begin{matrix} {C = \frac{3.5}{\left( {2\quad \pi \times 300 \times 10^{6}} \right)^{2} \times 3.25 \times 10^{- 9} \times \left( {3.5 + 4.20} \right)}} \\ {= {39.3\quad ({pF})}} \end{matrix}$

A circulator element which satisfies this condition is fabricated and thus a dual band lumped element circulator operable at octave frequencies of 300 MHz and 600 MHz is formed. Circuit constants of the resonance capacitance circuit connected to each port of the circulator instead of the conventional capacitor are determined with reference to the equation (22) as follows. $\begin{matrix} {C_{0} = {{39.3 \times \frac{1.30^{2} - 1}{1.62^{2} - 1}} = {16.7\quad ({pF})}}} \\ {C_{1} = {{16.7 \times \left( {\frac{1.62^{2}}{1.30^{2}} - 1} \right)} = {9.2\quad ({pF})}}} \end{matrix}$

 f _(s)=1.30 ×300=390(MHz)

$L_{1} = {\frac{1}{\left( {2\quad \pi \times 390 \times 10^{6}} \right)^{2} \times 9.2 \times 10^{- 12}} = {18.0\quad ({nH})}}$

The dual band circulator thus fabricated has a transfer characteristics as shown in FIG. 12. As will be understood from the figure, this measured transfer characteristics matches with the designed characteristics very well.

The aforementioned embodiment concerns a dual band circulator with two operation bands. It is known however that in a two-terminal resonance circuit with a plurality of resonance points, capacitive regions can be made by the number equal to the number of its resonance point pairs plus one. Therefore, it is apparent that a circulator with three or more operation bands at desired frequencies can be constructed by modifying the aforementioned embodiment.

FIG. 13 illustrates a resonance circuit connected to each port of a lumped element circulator of another embodiment according to the present invention.

As shown in the figure, this series-parallel resonance circuit has a series resonance circuit constituted by a resonance coil 131 with an inductance L₁ and a resonance capacitor 132 with a capacitance C₁ connected in series, a resonance capacitor 133 with a capacitance C₀ connected in parallel with the series resonance circuit, a resonance coil 134 with an inductance L₂ connected in series with the series resonance circuit, and a resonance capacitor 135 with a capacitance C₂ connected in parallel with the resonance coil 134 and the series resonance circuit. This two-terminal series-parallel resonance circuit is connected between each signal port and the grounded electrode of the circulator as well as the aforementioned embodiment.

This series-parallel resonance circuit has two pairs of series resonance point and parallel resonance point, and therefore is used for a circulator which requires three operation bands.

Many widely different embodiments of the present invention may be constructed without departing from the spirit and scope of the present invention. It should be understood that the present invention is not limited to the specific embodiments described in the specification, except as defined in the appended claims. 

What is claimed is:
 1. A lumped element circulator to be biased by a dc magnetic field and having a plurality of separated operation bands, comprising: a circulator element comprising a ferrite disc, a plurality of intersecting conductors having respective signal ports and a grounded terminal; and resonance circuits connected between said signal ports and said grounded terminal, respectively, each of said resonance circuits having a plurality of resonance points, the number of said operation bands being equal to the number of said resonance points of each of the resonance circuits, wherein said resonance circuits operate as capacitors within each of said operation bands.
 2. The circulator as claimed in claim 1, wherein each of said resonance circuits is a series-parallel resonance circuit having at least one pair of a series resonance point and a parallel resonance point.
 3. The circulator as claimed in claim 2, wherein the number of said operation bands is equal to the number of the pair of the series resonance point and the parallel resonance point plus one. 